Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,7,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(69.9364414204\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.6 | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.7.e.f.113.25 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 33.4715i | − | 1.23968i | −0.784727 | − | 0.619842i | \(-0.787197\pi\) | ||
0.784727 | − | 0.619842i | \(-0.212803\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 71.5877 | 0.572701 | 0.286351 | − | 0.958125i | \(-0.407558\pi\) | ||||
0.286351 | + | 0.958125i | \(0.407558\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −51.8109 | −0.151052 | −0.0755260 | − | 0.997144i | \(-0.524064\pi\) | ||||
−0.0755260 | + | 0.997144i | \(0.524064\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −391.339 | −0.536816 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −510.930 | −0.383870 | −0.191935 | − | 0.981408i | \(-0.561476\pi\) | ||||
−0.191935 | + | 0.981408i | \(0.561476\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2026.71i | 0.922489i | 0.887273 | + | 0.461244i | \(0.152597\pi\) | ||||
−0.887273 | + | 0.461244i | \(0.847403\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2396.14i | − | 0.709968i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8792.00 | 1.78954 | 0.894769 | − | 0.446528i | \(-0.147340\pi\) | ||||
0.894769 | + | 0.446528i | \(0.147340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6072.98 | − | 3188.23i | 0.885403 | − | 0.464824i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1734.19i | 0.187257i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −22866.7 | −1.87940 | −0.939702 | − | 0.341994i | \(-0.888898\pi\) | ||||
−0.939702 | + | 0.341994i | \(0.888898\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10500.2 | −0.672013 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 11302.0i | − | 0.574202i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 41913.8i | − | 1.71856i | −0.511510 | − | 0.859278i | \(-0.670914\pi\) | ||
0.511510 | − | 0.859278i | \(-0.329086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 49006.5i | − | 1.64501i | −0.568758 | − | 0.822505i | \(-0.692576\pi\) | ||
0.568758 | − | 0.822505i | \(-0.307424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17101.6i | 0.475877i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3709.02 | −0.0865077 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6756.83i | 0.133395i | 0.997773 | + | 0.0666973i | \(0.0212462\pi\) | ||||
−0.997773 | + | 0.0666973i | \(0.978754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 67836.9 | 1.14359 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39497.7i | 0.573087i | 0.958067 | + | 0.286543i | \(0.0925063\pi\) | ||||
−0.958067 | + | 0.286543i | \(0.907494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36231.6 | 0.455704 | 0.227852 | − | 0.973696i | \(-0.426830\pi\) | ||||
0.227852 | + | 0.973696i | \(0.426830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −28015.0 | −0.307435 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 142082. | 1.36850 | 0.684250 | − | 0.729247i | \(-0.260130\pi\) | ||||
0.684250 | + | 0.729247i | \(0.260130\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −114965. | −0.977183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 294281.i | − | 2.21846i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1332.46i | − | 0.00895009i | −0.999990 | − | 0.00447504i | \(-0.998576\pi\) | ||
0.999990 | − | 0.00447504i | \(-0.00142446\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −36576.3 | −0.219843 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −106715. | − | 203271.i | −0.576235 | − | 1.09762i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 90431.3i | − | 0.440314i | −0.975464 | − | 0.220157i | \(-0.929343\pi\) | ||
0.975464 | − | 0.220157i | \(-0.0706570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 111587. | 0.491613 | 0.245806 | − | 0.969319i | \(-0.420947\pi\) | ||||
0.245806 | + | 0.969319i | \(0.420947\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20275.6 | 0.0810871 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 145087.i | 0.528310i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 152853.i | 0.508216i | 0.967176 | + | 0.254108i | \(0.0817818\pi\) | ||||
−0.967176 | + | 0.254108i | \(0.918218\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 765382.i | 2.32987i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 572540.i | − | 1.59967i | −0.600219 | − | 0.799836i | \(-0.704920\pi\) | ||
0.600219 | − | 0.799836i | \(-0.295080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −231113. | −0.594094 | −0.297047 | − | 0.954863i | \(-0.596002\pi\) | ||||
−0.297047 | + | 0.954863i | \(0.596002\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 351457.i | 0.833084i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 26471.7 | 0.0579843 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 421938.i | − | 0.855790i | −0.903828 | − | 0.427895i | \(-0.859255\pi\) | ||
0.903828 | − | 0.427895i | \(-0.140745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −663581. | −1.24864 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −767322. | −1.34197 | −0.670986 | − | 0.741470i | \(-0.734129\pi\) | ||||
−0.670986 | + | 0.741470i | \(0.734129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 629399. | 1.02487 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.40292e6 | −2.13046 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 486637.i | − | 0.690296i | −0.938548 | − | 0.345148i | \(-0.887829\pi\) | ||
0.938548 | − | 0.345148i | \(-0.112171\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 105005.i | − | 0.139344i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.64032e6 | −2.03929 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 434750. | − | 228238.i | 0.507071 | − | 0.266205i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.34102e6i | 1.46933i | 0.678427 | + | 0.734667i | \(0.262662\pi\) | ||||
−0.678427 | + | 0.734667i | \(0.737338\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 199947. | 0.206067 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −733819. | −0.712238 | −0.356119 | − | 0.934441i | \(-0.615900\pi\) | ||||
−0.356119 | + | 0.934441i | \(0.615900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 536220.i | − | 0.490717i | −0.969432 | − | 0.245358i | \(-0.921094\pi\) | ||
0.969432 | − | 0.245358i | \(-0.0789057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 124146.i | 0.107242i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.62051e6i | 1.32282i | 0.750024 | + | 0.661410i | \(0.230042\pi\) | ||||
−0.750024 | + | 0.661410i | \(0.769958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 944227.i | − | 0.729117i | −0.931181 | − | 0.364558i | \(-0.881220\pi\) | ||
0.931181 | − | 0.364558i | \(-0.118780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 226161. | 0.165367 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.78541e6i | − | 1.23738i | −0.785636 | − | 0.618690i | \(-0.787664\pi\) | ||
0.785636 | − | 0.618690i | \(-0.212336\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.63697e6 | −1.07634 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 793129.i | − | 0.495206i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −455521. | −0.270314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.51051e6 | −0.852644 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.32205e6 | 0.710446 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.87024e6 | −0.957564 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.67124e6i | 1.30407i | 0.758189 | + | 0.652035i | \(0.226085\pi\) | ||||
−0.758189 | + | 0.652035i | \(0.773915\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.21273e6i | − | 0.564928i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.14444e6 | −1.84354 | −0.921769 | − | 0.387740i | \(-0.873256\pi\) | ||||
−0.921769 | + | 0.387740i | \(0.873256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −314646. | + | 165185.i | −0.133742 | + | 0.0702127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 809085.i | − | 0.328846i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.08052e6 | 1.19801 | 0.599007 | − | 0.800744i | \(-0.295562\pi\) | ||||
0.599007 | + | 0.800744i | \(0.295562\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −917454. | −0.341618 | −0.170809 | − | 0.985304i | \(-0.554638\pi\) | ||||
−0.170809 | + | 0.985304i | \(0.554638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.75569e6i | − | 1.69651i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.03551e6i | − | 0.354115i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.00051e6i | − | 0.984219i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.84803e6i | 1.21140i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.94518e6 | 0.890335 | 0.445168 | − | 0.895447i | \(-0.353144\pi\) | ||||
0.445168 | + | 0.895447i | \(0.353144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.51351e6i | − | 1.31094i | −0.755220 | − | 0.655471i | \(-0.772470\pi\) | ||
0.755220 | − | 0.655471i | \(-0.227530\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.44065e6 | −0.960652 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.50826e6i | − | 0.942099i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.86325e6 | 0.998284 | 0.499142 | − | 0.866520i | \(-0.333649\pi\) | ||||
0.499142 | + | 0.866520i | \(0.333649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −44599.5 | −0.0110953 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.18474e6 | 0.283888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.11582e6 | −0.719466 | −0.359733 | − | 0.933055i | \(-0.617132\pi\) | ||||
−0.359733 | + | 0.933055i | \(0.617132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.22426e6i | 0.272535i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.76930e6i | − | 1.23872i | −0.785106 | − | 0.619361i | \(-0.787392\pi\) | ||
0.785106 | − | 0.619361i | \(-0.212608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719264. | 0.149014 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.37659e6 | + | 1.24768e6i | −0.475298 | + | 0.249525i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.94440e6i | − | 0.568667i | −0.958725 | − | 0.284333i | \(-0.908228\pi\) | ||
0.958725 | − | 0.284333i | \(-0.0917723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 544025. | 0.101509 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.02687e6 | −0.545851 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.24741e6i | 1.43800i | 0.695011 | + | 0.718999i | \(0.255399\pi\) | ||||
−0.695011 | + | 0.718999i | \(0.744601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.92358e6i | − | 0.661678i | −0.943687 | − | 0.330839i | \(-0.892668\pi\) | ||
0.943687 | − | 0.330839i | \(-0.107332\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.73497e6i | − | 0.609444i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 483706.i | 0.0763952i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.49210e6 | −0.686950 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 585567.i | 0.0867344i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.67486e6 | −0.670917 | −0.335458 | − | 0.942055i | \(-0.608891\pi\) | ||||
−0.335458 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 488419.i | 0.0679392i | 0.999423 | + | 0.0339696i | \(0.0108149\pi\) | ||||
−0.999423 | + | 0.0339696i | \(0.989185\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.85628e6 | 0.654938 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.02303e7 | −1.33810 | −0.669049 | − | 0.743218i | \(-0.733298\pi\) | ||||
−0.669049 | + | 0.743218i | \(0.733298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.76883e6 | 0.605136 | 0.302568 | − | 0.953128i | \(-0.402156\pi\) | ||||
0.302568 | + | 0.953128i | \(0.402156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.11620e6 | 0.630027 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.17159e6i | 0.259591i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.82755e6i | 0.328207i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.94863e6 | 1.00889 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.10287e6 | + | 1.62896e6i | −0.339879 | + | 0.178432i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.81102e6i | − | 0.192786i | −0.995343 | − | 0.0963929i | \(-0.969269\pi\) | ||
0.995343 | − | 0.0963929i | \(-0.0307305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.91638e7 | −1.98309 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.59374e6 | 0.260982 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.53907e6i | 0.248482i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.73568e6i | 0.736489i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.78188e7i | 1.65083i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.03795e6i | − | 0.273946i | −0.990575 | − | 0.136973i | \(-0.956263\pi\) | ||
0.990575 | − | 0.136973i | \(-0.0437374\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.10914e6 | 0.360747 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.30769e7i | − | 1.11797i | −0.829179 | − | 0.558983i | \(-0.811192\pi\) | ||
0.829179 | − | 0.558983i | \(-0.188808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.33095e6 | 0.693727 | 0.346863 | − | 0.937916i | \(-0.387247\pi\) | ||||
0.346863 | + | 0.937916i | \(0.387247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 886048.i | − | 0.0718822i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.12149e7 | 1.67715 | 0.838577 | − | 0.544783i | \(-0.183388\pi\) | ||||
0.838577 | + | 0.544783i | \(0.183388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.01713e7 | 0.783742 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.41229e7 | −1.06091 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.03319e7 | 0.756807 | 0.378403 | − | 0.925641i | \(-0.376473\pi\) | ||||
0.378403 | + | 0.925641i | \(0.376473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.06626e6i | 0.504823i | 0.967620 | + | 0.252411i | \(0.0812236\pi\) | ||||
−0.967620 | + | 0.252411i | \(0.918776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.39719e7i | 0.973722i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.23005e6 | −0.559634 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.46161e6 | + | 1.23082e7i | 0.428795 | + | 0.816774i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.56834e7i | 1.66362i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.59405e6 | 0.353757 | 0.176878 | − | 0.984233i | \(-0.443400\pi\) | ||||
0.176878 | + | 0.984233i | \(0.443400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.16833e7 | 0.721446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 2.10669e7i | − | 1.27052i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.74163e7i | 1.61514i | 0.589775 | + | 0.807568i | \(0.299217\pi\) | ||||
−0.589775 | + | 0.807568i | \(0.700783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 350077.i | − | 0.0201495i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.64025e7i | 0.922547i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.80126e7 | −0.990168 | −0.495084 | − | 0.868845i | \(-0.664863\pi\) | ||||
−0.495084 | + | 0.868845i | \(0.664863\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 95387.8i | − | 0.00512573i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.62885e7 | −0.855749 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.68264e6i | − | 0.343314i | −0.985157 | − | 0.171657i | \(-0.945088\pi\) | ||
0.985157 | − | 0.171657i | \(-0.0549120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.73961e6 | 0.238141 | 0.119071 | − | 0.992886i | \(-0.462009\pi\) | ||||
0.119071 | + | 0.992886i | \(0.462009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.51469e6 | −0.172742 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.36488e6 | 0.257965 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.14107e7 | 1.94838 | 0.974190 | − | 0.225730i | \(-0.0724767\pi\) | ||||
0.974190 | + | 0.225730i | \(0.0724767\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.91781e7i | 0.883067i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.00129e7i | − | 0.901966i | −0.892533 | − | 0.450983i | \(-0.851073\pi\) | ||
0.892533 | − | 0.450983i | \(-0.148927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.23503e6 | 0.319213 | 0.159607 | − | 0.987181i | \(-0.448977\pi\) | ||||
0.159607 | + | 0.987181i | \(0.448977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.63945e6 | − | 1.45517e7i | −0.330010 | − | 0.628608i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.04641e6i | − | 0.0865660i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.31618e7 | 2.20245 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.48860e7 | 1.82151 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.07240e6i | − | 0.241411i | −0.992688 | − | 0.120706i | \(-0.961484\pi\) | ||
0.992688 | − | 0.120706i | \(-0.0385157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6.47377e6i | − | 0.252169i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.77455e6i | 0.220419i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 4.63442e7i | − | 1.73373i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.87719e6 | −0.0688350 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.45620e7i | 0.882949i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.98824e6 | 0.281547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.92735e7i | 0.666109i | 0.942908 | + | 0.333054i | \(0.108079\pi\) | ||||
−0.942908 | + | 0.333054i | \(0.891921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.79481e7 | −0.608334 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.31848e7 | 0.438321 | 0.219160 | − | 0.975689i | \(-0.429668\pi\) | ||||
0.219160 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.27464e7 | −1.39401 | −0.697006 | − | 0.717065i | \(-0.745485\pi\) | ||||
−0.697006 | + | 0.717065i | \(0.745485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.45148e6 | 0.0464387 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.26029e7i | − | 1.65132i | −0.564166 | − | 0.825662i | \(-0.690802\pi\) | ||
0.564166 | − | 0.825662i | \(-0.309198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.14151e7i | 0.659701i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.42409e7 | 1.63988 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.33937e7 | − | 2.80309e7i | 1.58446 | − | 0.831821i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.12809e7i | − | 0.619925i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.16047e7 | −0.903874 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.36138e6 | −0.206715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.26389e7i | 1.45152i | 0.687948 | + | 0.725760i | \(0.258512\pi\) | ||||
−0.687948 | + | 0.725760i | \(0.741488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.64421e6i | − | 0.0716083i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.09424e7i | 0.291056i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.10163e7i | − | 1.85553i | −0.373162 | − | 0.927766i | \(-0.621726\pi\) | ||
0.373162 | − | 0.927766i | \(-0.378274\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.97603e7 | −1.53396 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.50389e7i | 0.631469i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.20519e7 | 0.298658 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.47919e7i | 1.33432i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.00746e7 | −0.719798 | −0.359899 | − | 0.932991i | \(-0.617189\pi\) | ||||
−0.359899 | + | 0.932991i | \(0.617189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.08341e7 | −1.43110 | −0.715551 | − | 0.698560i | \(-0.753824\pi\) | ||||
−0.715551 | + | 0.698560i | \(0.753824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.29059e7 | 0.529695 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.29214e7 | 0.748436 | 0.374218 | − | 0.927341i | \(-0.377911\pi\) | ||||
0.374218 | + | 0.927341i | \(0.377911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.09868e7i | − | 0.916134i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.52470e7i | 0.335103i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.25010e7 | 1.56697 | 0.783485 | − | 0.621410i | \(-0.213440\pi\) | ||||
0.783485 | + | 0.621410i | \(0.213440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.67163e7 | − | 3.87241e7i | 0.567877 | − | 0.823113i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.05590e7i | 1.05701i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.65448e7 | −0.340238 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −719204. | −0.0145497 | −0.00727485 | − | 0.999974i | \(-0.502316\pi\) | ||||
−0.00727485 | + | 0.999974i | \(0.502316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.54570e7i | − | 0.307642i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 69036.0i | 0.00135193i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.30946e7i | − | 1.60120i | −0.599197 | − | 0.800601i | \(-0.704514\pi\) | ||
0.599197 | − | 0.800601i | \(-0.295486\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.25997e7i | 1.18708i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.49471e7 | 1.58535 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.81125e7i | − | 0.332707i | −0.986066 | − | 0.166353i | \(-0.946801\pi\) | ||
0.986066 | − | 0.166353i | \(-0.0531992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.94102e7 | 1.61663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.46626e7i | 0.794965i | 0.917610 | + | 0.397482i | \(0.130116\pi\) | ||||
−0.917610 | + | 0.397482i | \(0.869884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.89505e6 | 0.0332077 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.41788e7 | −0.244629 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.94692e7 | 0.330750 | 0.165375 | − | 0.986231i | \(-0.447117\pi\) | ||||
0.165375 | + | 0.986231i | \(0.447117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.01044e8 | −3.36327 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.38720e8i | 2.28540i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.02055e7i | − | 0.490112i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.23981e7 | −1.15706 | −0.578529 | − | 0.815662i | \(-0.696373\pi\) | ||||
−0.578529 | + | 0.815662i | \(0.696373\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.52898e6 | + | 1.05317e7i | 0.0870415 | + | 0.165798i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.82777e7i | − | 0.438542i | −0.975664 | − | 0.219271i | \(-0.929632\pi\) | ||
0.975664 | − | 0.219271i | \(-0.0703678\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.93218e7 | 1.51750 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.75042e7 | −0.715100 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.45227e6i | − | 0.0512061i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.47597e7i | − | 0.508050i | −0.967198 | − | 0.254025i | \(-0.918245\pi\) | ||
0.967198 | − | 0.254025i | \(-0.0817545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.03109e8i | − | 1.48516i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.68533e6i | 0.0665104i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.49308e7 | −0.768549 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.07085e7i | 0.423498i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00892e7 | −0.816872 | −0.408436 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408436 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.86723e7i | 0.786297i | 0.919475 | + | 0.393149i | \(0.128614\pi\) | ||||
−0.919475 | + | 0.393149i | \(0.871386\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.56021e7 | −0.734633 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.23179e7 | −1.20259 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.78141e6 | −0.0742591 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.46599e7 | −0.438991 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.26614e8i | 1.58143i | 0.612184 | + | 0.790715i | \(0.290291\pi\) | ||||
−0.612184 | + | 0.790715i | \(0.709709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.14600e7i | 0.757057i | 0.925590 | + | 0.378529i | \(0.123570\pi\) | ||||
−0.925590 | + | 0.378529i | \(0.876430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.00432e8 | −1.22012 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.38869e8 | + | 7.29043e7i | −1.66403 | + | 0.873593i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.93952e7i | 0.229246i | 0.993409 | + | 0.114623i | \(0.0365660\pi\) | ||||
−0.993409 | + | 0.114623i | \(0.963434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.49901e7 | 0.524567 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.20889e8 | 1.39052 | 0.695259 | − | 0.718759i | \(-0.255290\pi\) | ||||
0.695259 | + | 0.718759i | \(0.255290\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 3.48372e7i | − | 0.395333i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 9.85796e7i | − | 1.10373i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.67006e7i | − | 0.515921i | −0.966155 | − | 0.257961i | \(-0.916950\pi\) | ||
0.966155 | − | 0.257961i | \(-0.0830505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.01806e7i | − | 0.219991i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.51074e8 | −1.62515 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 7.51710e6i | − | 0.0798024i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.41054e7 | 0.147787 | 0.0738934 | − | 0.997266i | \(-0.476458\pi\) | ||||
0.0738934 | + | 0.997266i | \(0.476458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 9.93674e7i | − | 1.02756i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.97662e7 | 0.507962 | 0.253981 | − | 0.967209i | \(-0.418260\pi\) | ||||
0.253981 | + | 0.967209i | \(0.418260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.83674e7 | 0.991079 | 0.495539 | − | 0.868586i | \(-0.334970\pi\) | ||||
0.495539 | + | 0.868586i | \(0.334970\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.17427e8 | −1.16790 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.59046e7 | 0.647090 | 0.323545 | − | 0.946213i | \(-0.395125\pi\) | ||||
0.323545 | + | 0.946213i | \(0.395125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.91942e6i | − | 0.0767671i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.29309e8i | − | 1.23756i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.85118e7 | −0.174931 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.37675e7 | + | 3.34771e7i | −0.595003 | + | 0.312368i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 521444.i | 0.00480455i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.08450e7 | −0.371649 | −0.185824 | − | 0.982583i | \(-0.559496\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.36941e7 | −0.123055 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3.96551e7i | − | 0.351931i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.60006e7i | 0.841490i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.20128e7i | − | 0.363743i | −0.983322 | − | 0.181871i | \(-0.941785\pi\) | ||
0.983322 | − | 0.181871i | \(-0.0582155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.04291e8i | 0.891910i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.24183e8 | −1.04910 | −0.524549 | − | 0.851380i | \(-0.675766\pi\) | ||||
−0.524549 | + | 0.851380i | \(0.675766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.68507e8i | − | 3.07542i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.43137e7 | 0.118015 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.96638e7i | 0.241634i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.52533e7 | 0.122762 | 0.0613809 | − | 0.998114i | \(-0.480450\pi\) | ||||
0.0613809 | + | 0.998114i | \(0.480450\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.93107e8 | −1.53562 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.71504e8 | 1.34763 | 0.673814 | − | 0.738901i | \(-0.264655\pi\) | ||||
0.673814 | + | 0.738901i | \(0.264655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.25324e7 | −0.407899 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 2.40748e7i | − | 0.184731i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7.95755e7i | − | 0.603429i | −0.953398 | − | 0.301714i | \(-0.902441\pi\) | ||
0.953398 | − | 0.301714i | \(-0.0975589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.19742e7 | 0.0897392 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.60334e7 | − | 6.86369e7i | −0.266903 | − | 0.508400i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.83867e7i | − | 0.281034i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.25939e7 | −0.525326 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.85532e7 | −0.704967 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.40151e8i | 1.69813i | 0.528288 | + | 0.849065i | \(0.322834\pi\) | ||||
−0.528288 | + | 0.849065i | \(0.677166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.35375e7i | 0.583951i | 0.956426 | + | 0.291975i | \(0.0943125\pi\) | ||||
−0.956426 | + | 0.291975i | \(0.905687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.82093e7i | − | 0.125839i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.30865e8i | − | 2.94381i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.74851e8 | 2.53216 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.53893e7i | 0.236368i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.00503e7 | −0.528666 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.16009e8i | 0.757581i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.76053e8 | 1.78266 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.87389e7 | 0.375111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.33819e8 | −0.845133 | −0.422567 | − | 0.906332i | \(-0.638871\pi\) | ||||
−0.422567 | + | 0.906332i | \(0.638871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.31328e8 | −0.820271 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.75950e7i | − | 0.417566i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.97530e7i | 0.120690i | 0.998178 | + | 0.0603449i | \(0.0192200\pi\) | ||||
−0.998178 | + | 0.0603449i | \(0.980780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.36682e7 | −0.263905 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.33631e8 | − | 2.54542e8i | −0.798826 | − | 1.52161i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.18610e7i | 0.129269i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.61903e7 | 0.0947059 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.64574e7 | 0.0952349 | 0.0476175 | − | 0.998866i | \(-0.484837\pi\) | ||||
0.0476175 | + | 0.998866i | \(0.484837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.34309e7i | 0.420382i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.50357e8i | 0.851600i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.80150e6i | 0.0156988i | 0.999969 | + | 0.00784939i | \(0.00249856\pi\) | ||||
−0.999969 | + | 0.00784939i | \(0.997501\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.27813e8i | − | 0.708648i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.43807e7 | 0.188610 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.04615e8i | − | 0.567881i | −0.958842 | − | 0.283941i | \(-0.908358\pi\) | ||
0.958842 | − | 0.283941i | \(-0.0916418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.28204e8 | −1.22579 | −0.612893 | − | 0.790166i | \(-0.709994\pi\) | ||||
−0.612893 | + | 0.790166i | \(0.709994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.56474e8i | 0.831725i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.40105e8 | 1.26298 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.96754e8 | 1.54479 | 0.772395 | − | 0.635142i | \(-0.219058\pi\) | ||||
0.772395 | + | 0.635142i | \(0.219058\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.63481e7 | 0.0842231 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.97556e7 | 0.202708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 680795.i | 0.00343567i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.67783e7i | − | 0.283605i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.18280e7 | 0.0584785 | 0.0292392 | − | 0.999572i | \(-0.490692\pi\) | ||||
0.0292392 | + | 0.999572i | \(0.490692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.56244e8 | − | 2.97615e8i | −0.764640 | − | 1.45650i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.42422e8i | 1.65882i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.29365e8 | 0.620374 | 0.310187 | − | 0.950676i | \(-0.399608\pi\) | ||||
0.310187 | + | 0.950676i | \(0.399608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.26097e7 | −0.154809 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.59620e8i | − | 0.750177i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.75609e7i | 0.128237i | 0.997942 | + | 0.0641184i | \(0.0204235\pi\) | ||||
−0.997942 | + | 0.0641184i | \(0.979576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.62146e7i | 0.120759i | 0.998175 | + | 0.0603796i | \(0.0192311\pi\) | ||||
−0.998175 | + | 0.0603796i | \(0.980769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.98171e7i | − | 0.272818i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.08134e8 | −0.488310 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.81199e7i | − | 0.0810196i | −0.999179 | − | 0.0405098i | \(-0.987102\pi\) | ||
0.999179 | − | 0.0405098i | \(-0.0128982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.26864e7 | 0.321811 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.87958e8i | 1.26243i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.45891e8 | −0.633354 | −0.316677 | − | 0.948533i | \(-0.602567\pi\) | ||||
−0.316677 | + | 0.948533i | \(0.602567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.46422e7 | 0.406873 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.65303e8 | 1.12950 | 0.564752 | − | 0.825261i | \(-0.308972\pi\) | ||||
0.564752 | + | 0.825261i | \(0.308972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.21064e7 | −0.177532 | −0.0887658 | − | 0.996053i | \(-0.528292\pi\) | ||||
−0.0887658 | + | 0.996053i | \(0.528292\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.58440e8i | 1.07916i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.52131e7i | 0.104271i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.01795e7 | 0.123615 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.45238e7 | + | 1.03858e8i | 0.221199 | + | 0.421343i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.94061e7i | 0.238715i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.37249e7 | −0.0944314 | −0.0472157 | − | 0.998885i | \(-0.515035\pi\) | ||||
−0.0472157 | + | 0.998885i | \(0.515035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.06173e7 | −0.238993 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.91227e8i | 0.746843i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.33000e8i | − | 0.901441i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.24057e8i | 0.858729i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.10625e7i | 0.269815i | 0.990858 | + | 0.134908i | \(0.0430737\pi\) | ||||
−0.990858 | + | 0.134908i | \(0.956926\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.19477e7 | −0.195404 | −0.0977021 | − | 0.995216i | \(-0.531149\pi\) | ||||
−0.0977021 | + | 0.995216i | \(0.531149\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 8.68162e7i | − | 0.323535i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.98051e8 | 0.731246 | 0.365623 | − | 0.930763i | \(-0.380856\pi\) | ||||
0.365623 | + | 0.930763i | \(0.380856\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.62041e7i | 0.169023i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.49863e7 | 0.308039 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.19882e8 | 0.430540 | 0.215270 | − | 0.976555i | \(-0.430937\pi\) | ||||
0.215270 | + | 0.976555i | \(0.430937\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.96691e8 | −1.05580 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.04433e7 | 0.318919 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.57886e8i | 1.59993i | 0.600045 | + | 0.799966i | \(0.295149\pi\) | ||||
−0.600045 | + | 0.799966i | \(0.704851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.03652e8i | 1.05141i | 0.850667 | + | 0.525705i | \(0.176198\pi\) | ||||
−0.850667 | + | 0.525705i | \(0.823802\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.96422e8 | 2.04651 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.25248e7 | + | 1.18252e7i | −0.0765942 | + | 0.0402109i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.58432e8i | 3.22986i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.01684e8 | −0.339607 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.70131e7 | −0.188715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.98432e8i | − | 1.63516i | −0.575813 | − | 0.817582i | \(-0.695314\pi\) | ||
0.575813 | − | 0.817582i | \(-0.304686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.18674e8i | 0.385871i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.01610e8i | 0.327470i | 0.986504 | + | 0.163735i | \(0.0523542\pi\) | ||||
−0.986504 | + | 0.163735i | \(0.947646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.94795e7i | − | 0.221946i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.37705e8 | −1.38593 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.15235e8i | − | 0.675539i | −0.941229 | − | 0.337770i | \(-0.890328\pi\) | ||
0.941229 | − | 0.337770i | \(-0.109672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.20527e8 | 0.686104 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.78849e8i | − | 0.860001i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.70051e6 | 0.00825636 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.21330e8 | −1.27699 | −0.638497 | − | 0.769625i | \(-0.720443\pi\) | ||||
−0.638497 | + | 0.769625i | \(0.720443\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.03594e7 | −0.0311269 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.56784e7 | −0.195645 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.47264e8i | 1.02556i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 7.10093e8i | − | 2.07914i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.22655e8 | 1.80756 | 0.903782 | − | 0.427994i | \(-0.140780\pi\) | ||||
0.903782 | + | 0.427994i | \(0.140780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.15423e7 | + | 4.10341e7i | 0.0620050 | + | 0.118108i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 3.40448e8i | − | 0.971592i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.80198e7 | 0.107585 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.65405e8 | 0.464097 | 0.232049 | − | 0.972704i | \(-0.425457\pi\) | ||||
0.232049 | + | 0.972704i | \(0.425457\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.65121e8i | 0.459402i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.12062e9i | 3.09164i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.41295e7i | − | 0.202802i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.45823e8i | − | 0.938201i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.39243e8 | 0.912692 | 0.456346 | − | 0.889802i | \(-0.349158\pi\) | ||||
0.456346 | + | 0.889802i | \(0.349158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.77820e7i | 0.0741238i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.36518e8 | 0.625820 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.40104e8i | 1.15489i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.80897e8 | −0.991297 | −0.495649 | − | 0.868523i | \(-0.665070\pi\) | ||||
−0.495649 | + | 0.868523i | \(0.665070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.60923e7 | −0.0415369 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.18549e8 | 0.815499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.61548e8 | −0.664108 | −0.332054 | − | 0.943260i | \(-0.607742\pi\) | ||||
−0.332054 | + | 0.943260i | \(0.607742\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.75472e8i | 0.693769i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.80970e7i | − | 0.195089i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.88512e8 | −1.21044 | −0.605218 | − | 0.796060i | \(-0.706914\pi\) | ||||
−0.605218 | + | 0.796060i | \(0.706914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.11972e8 | − | 2.16279e8i | 1.01254 | − | 0.531570i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.47484e8i | − | 0.847166i | −0.905857 | − | 0.423583i | \(-0.860772\pi\) | ||
0.905857 | − | 0.423583i | \(-0.139228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.10839e8 | 0.509896 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.00283e8 | 0.720392 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8.39602e7i | − | 0.199815i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 5.37037e8i | − | 1.26790i | −0.773375 | − | 0.633949i | \(-0.781433\pi\) | ||
0.773375 | − | 0.633949i | \(-0.218567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.87241e8i | − | 0.438547i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.23111e8i | − | 0.750778i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.06677e7 | −0.0937479 | −0.0468740 | − | 0.998901i | \(-0.514926\pi\) | ||||
−0.0468740 | + | 0.998901i | \(0.514926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3.91057e8i | − | 0.894365i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.59362e7 | 0.0815413 | 0.0407707 | − | 0.999169i | \(-0.487019\pi\) | ||||
0.0407707 | + | 0.999169i | \(0.487019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.89212e7i | 0.110135i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.46308e8 | −0.550167 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.83278e8 | 0.406185 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.90636e8 | 1.29880 | 0.649398 | − | 0.760449i | \(-0.275021\pi\) | ||||
0.649398 | + | 0.760449i | \(0.275021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.17663e8 | 2.00226 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.37852e8i | 1.16446i | 0.813025 | + | 0.582229i | \(0.197819\pi\) | ||||
−0.813025 | + | 0.582229i | \(0.802181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.14578e8i | 1.10547i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.17176e7 | −0.0249790 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.25928e8 | + | 2.39869e8i | 0.266385 | + | 0.507413i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.92528e8i | 0.614065i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.73711e8 | −0.986798 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.76561e8 | 0.571719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.32782e8i | − | 0.887860i | −0.896061 | − | 0.443930i | \(-0.853584\pi\) | ||
0.896061 | − | 0.443930i | \(-0.146416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.02908e8i | 1.22750i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.25037e7i | 0.186909i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.26154e8i | 0.453507i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.19277e6 | −0.00635428 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 7.42582e8i | − | 1.46680i | −0.679800 | − | 0.733398i | \(-0.737933\pi\) | ||
0.679800 | − | 0.733398i | \(-0.262067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24918e9 | 2.44898 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.90440e8i | 0.370562i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.18083e8 | 0.228055 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.48131e7 | 0.162583 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.23678e8 | −0.425600 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.67711e8 | 0.505616 | 0.252808 | − | 0.967516i | \(-0.418646\pi\) | ||||
0.252808 | + | 0.967516i | \(0.418646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.36834e8i | 1.19389i | 0.802283 | + | 0.596944i | \(0.203619\pi\) | ||||
−0.802283 | + | 0.596944i | \(0.796381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.58642e8i | − | 0.295220i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.23055e8 | −0.412039 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.20034e8 | − | 1.15515e8i | 0.403481 | − | 0.211822i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.10927e7i | 0.0748020i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.37818e7 | 0.0610454 | 0.0305227 | − | 0.999534i | \(-0.490283\pi\) | ||||
0.0305227 | + | 0.999534i | \(0.490283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.68249e8 | 1.01939 | 0.509693 | − | 0.860356i | \(-0.329759\pi\) | ||||
0.509693 | + | 0.860356i | \(0.329759\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.79570e8i | − | 0.319796i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.00761e8i | − | 1.06215i | −0.847325 | − | 0.531074i | \(-0.821788\pi\) | ||
0.847325 | − | 0.531074i | \(-0.178212\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.05498e8i | − | 0.887270i | −0.896208 | − | 0.443635i | \(-0.853689\pi\) | ||
0.896208 | − | 0.443635i | \(-0.146311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.38608e9i | − | 2.41537i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.01077e9 | −1.74871 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.13011e8i | − | 0.709418i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.53872e8 | −0.944568 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.06603e7i | 0.0688469i | 0.999407 | + | 0.0344235i | \(0.0109595\pi\) | ||||
−0.999407 | + | 0.0344235i | \(0.989041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.16195e9 | −1.95343 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.69860e8 | −1.11815 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.14904e7 | 0.0853407 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.82609e7 | 0.128794 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 2.42167e8i | − | 0.395724i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.54507e8i | − | 0.250702i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.06743e8 | −0.977592 | −0.488796 | − | 0.872398i | \(-0.662564\pi\) | ||||
−0.488796 | + | 0.872398i | \(0.662564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.70135e8 | + | 8.93183e7i | −0.272204 | + | 0.142903i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.60934e8i | 0.255685i | 0.991794 | + | 0.127843i | \(0.0408053\pi\) | ||||
−0.991794 | + | 0.127843i | \(0.959195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.17471e8 | 1.44748 | 0.723740 | − | 0.690073i | \(-0.242421\pi\) | ||||
0.723740 | + | 0.690073i | \(0.242421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.84964e7 | −0.107314 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.03177e9i | 1.60528i | 0.596466 | + | 0.802638i | \(0.296571\pi\) | ||||
−0.596466 | + | 0.802638i | \(0.703429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 2.10782e8i | − | 0.325676i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.77940e9i | − | 2.73034i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.15581e8i | 0.328512i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.09787e8 | −0.468823 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.24794e8i | − | 0.788762i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.68989e7 | 0.144642 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.27402e9i | 1.88876i | 0.328850 | + | 0.944382i | \(0.393339\pi\) | ||||
−0.328850 | + | 0.944382i | \(0.606661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.03252e8 | −0.299274 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.06039e8 | −0.155074 | −0.0775370 | − | 0.996989i | \(-0.524706\pi\) | ||||
−0.0775370 | + | 0.996989i | \(0.524706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.63067e8 | −0.963108 | −0.481554 | − | 0.876416i | \(-0.659927\pi\) | ||||
−0.481554 | + | 0.876416i | \(0.659927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.16686e8 | −0.312609 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.90226e8i | 0.989056i | 0.869162 | + | 0.494528i | \(0.164659\pi\) | ||||
−0.869162 | + | 0.494528i | \(0.835341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.38399e8i | − | 0.196983i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.39044e8 | 0.479317 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.62860e8 | − | 4.52989e8i | 1.21167 | − | 0.636112i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.90412e8i | 0.823543i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.55121e9 | −2.14928 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.05405e9 | −2.82704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.17150e7i | − | 0.0160165i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.28324e7i | 0.0853336i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.80880e8i | − | 0.378944i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7.18182e8i | − | 0.962527i | −0.876576 | − | 0.481263i | \(-0.840178\pi\) | ||
0.876576 | − | 0.481263i | \(-0.159822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.87172e8 | 0.382340 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.37912e9i | 1.82410i | 0.410083 | + | 0.912048i | \(0.365500\pi\) | ||||
−0.410083 | + | 0.912048i | \(0.634500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.92048e8 | 0.515142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 2.67378e8i | − | 0.349030i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.14727e8 | 0.278470 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.20524e9 | −1.55284 | −0.776419 | − | 0.630217i | \(-0.782966\pi\) | ||||
−0.776419 | + | 0.630217i | \(0.782966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.45111e8 | 0.825764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.16037e9 | 1.47568 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 7.09482e7i | − | 0.0896429i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.09843e8i | 0.263425i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.36214e7 | −0.0544067 | −0.0272033 | − | 0.999630i | \(-0.508660\pi\) | ||||
−0.0272033 | + | 0.999630i | \(0.508660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.98178e8 | + | 3.66534e8i | −0.865201 | + | 0.454218i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 4.41314e8i | − | 0.543379i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.21579e8 | −0.393417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.87075e8 | 0.713633 | 0.356817 | − | 0.934174i | \(-0.383862\pi\) | ||||
0.356817 | + | 0.934174i | \(0.383862\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.43078e9i | 1.72813i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.17508e8i | 0.741094i | 0.928814 | + | 0.370547i | \(0.120830\pi\) | ||||
−0.928814 | + | 0.370547i | \(0.879170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 9.03183e8i | − | 1.07706i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.19194e7i | 0.0496729i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.09790e9 | 1.29275 | 0.646375 | − | 0.763020i | \(-0.276284\pi\) | ||||
0.646375 | + | 0.763020i | \(0.276284\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.68398e8i | − | 0.548045i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.76070e9 | −2.04712 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.46976e9i | 1.69812i | 0.528299 | + | 0.849058i | \(0.322830\pi\) | ||||
−0.528299 | + | 0.849058i | \(0.677170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.34662e8 | −0.384235 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.16793e8 | 0.817821 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.59604e8 | −0.180962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.51413e9 | −1.70606 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.34169e8i | − | 0.710111i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.49647e7i | 0.0389089i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.38188e9 | −1.52824 | −0.764121 | − | 0.645072i | \(-0.776827\pi\) | ||||
−0.764121 | + | 0.645072i | \(0.776827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.38236e8 | − | 1.78716e9i | −1.03119 | − | 1.96423i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.08548e9i | 1.18567i | 0.805326 | + | 0.592833i | \(0.201991\pi\) | ||||
−0.805326 | + | 0.592833i | \(0.798009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.75341e7 | 0.0516020 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.12301e8 | −0.768511 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.78848e8i | − | 0.942388i | −0.882029 | − | 0.471194i | \(-0.843823\pi\) | ||
0.882029 | − | 0.471194i | \(-0.156177\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.48638e8i | 0.264984i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.69513e8i | 0.391401i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.03866e8i | − | 0.635740i | −0.948134 | − | 0.317870i | \(-0.897032\pi\) | ||
0.948134 | − | 0.317870i | \(-0.102968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.32360e8 | −0.766330 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.46396e8i | 0.256261i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.28498e8 | −0.856452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.53282e8i | 0.465745i | 0.972507 | + | 0.232872i | \(0.0748124\pi\) | ||||
−0.972507 | + | 0.232872i | \(0.925188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.76190e9 | 1.79942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.41389e8 | 0.346562 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.50572e8 | −0.151935 | −0.0759675 | − | 0.997110i | \(-0.524205\pi\) | ||||
−0.0759675 | + | 0.997110i | \(0.524205\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.63659e7 | 0.0765954 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 304.7.e.f.113.6 | 30 | ||
4.3 | odd | 2 | 152.7.e.a.113.25 | yes | 30 | ||
19.18 | odd | 2 | inner | 304.7.e.f.113.25 | 30 | ||
76.75 | even | 2 | 152.7.e.a.113.6 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.7.e.a.113.6 | ✓ | 30 | 76.75 | even | 2 | ||
152.7.e.a.113.25 | yes | 30 | 4.3 | odd | 2 | ||
304.7.e.f.113.6 | 30 | 1.1 | even | 1 | trivial | ||
304.7.e.f.113.25 | 30 | 19.18 | odd | 2 | inner |